Approximation of multiple switched flow systems for the purpose of control synthesis

Switched flow systems exhibit a continuous state evolving w.r.t. continuous time. However, a purely discrete interface to the environment is provided, acting on input events by switching between a finite number of flows and generating output events whenever the continuous state crosses certain boundaries. Here, a practically important task is the synthesis of a supervisory controller enforcing a specification in terms of input and output events to be met. A well known approach is so called approximation based synthesis, where the switched flow system is approximately realized by a finite automation. In the situation of multiple switched flow systems the question arises first, how to approximate the individual systems, and second, how to compose the approximations in order to finally apply a synthesis scheme. It turns out that retaining clock time on the approximation level leads to a suitable overall procedure.